METHODS OF INTEEPOLATION. 



325 



by using- this table, for care lias been taken to make the seventh decimal 

 tigure always correct to its nearest value. This would not be the case 

 if the logarithm were taken in the usual way from a seven-figure table, 

 and multiplied by the index of the power required, for then the last 

 figure might be in error by an amount not exceeding half the number 

 of units in the index. For instance, an ordinary table gives 



log (1.5)«= 8 X .1700913 = 1.4087304 

 whereas the true value is 1.4087301. 



Logarithms of poivers of integers and half-integers from to 50. 



X 



loga;2 



log x^ 



loga;^ 



loga;= 



loga;8 



logo;' 



log rcS 



0.5 



1. 3979430 



1.0969100 



2. 7958800 



2. 4948500 



2. 1938200 



3. 8927900 



3. 5917600 



1.0 



. 0000000 



. 0000000 



. 0000000 



. OOOOOCO 



. OOOOOOO 



. OOOOOOO 



. OOOOOOO 



1.5 



. 3521825 



. 5282738 



. 7043650 



. 8804563 



1. 0565476 



1. 2326388 



1. 4087301 



'2.0 



. 6020C00 



. 903'J900 



1.2041200 



1. 5051."00 



1.8061800 



2. 1072100 



2. 4082400 



2.5 



. 79588U0 



1. 1938200 



1. 5917600 



1.9897000 



2. 3876401 



2. 7855801 



3.18.35201 



3.0 



. 9542425 



1. 401 3038 



1. 9084850 



2. 3850063 



2. 8627275 



3. 3398488 



3. 8169700 



3.5 



1.0881361 



1. 6322041 



2. 1762722 



2. 7203402 



3. 2644083 



3. 8!184763 



4. 3525444 



4.0 



1.2041200 



1.8001800 



2. 4C82400 



3. 0103000 



3. 6123599 



4.2144199 



4. 81(!4799 



4.5 



1. 3064250 



1. 9596375 



2. 6128501 



3. 2660626 



3. 9192751 



4. .5724876 



5. 2257001 



5.0 



1.39794C0 



2.0969100 



2. 7958800 



3. 4948500 



4. 1938200 



4. 8927900 



5.5917000 



5. 5 



1. 4807254 



2.2210881 



2. 9614508 



3.7018134 



4. 4421761 



5. 1825388 



5. 92;29015 



CO 



1. 5563025 



2. 3344538 



3. 1126050 



3. 8907563 



4. 6689075 



5. 4470588 



6. 2252100 



6.5 



1. 6258267 



2. 4387401 



3.2516534 



4. 0645668 



4. 8774801 



5. 6903935 



6. 5033069 



7.0 



1. 6901961 



2. 5352941 



3. 3803922 



4. 2254902 



5. 0705882 



5. 9156863 



0. 7607843 



7.5 



1. 7501225 



2. 6251838 



3. 5002451 



4. 3753063 



5. 2503676 



6. 1254288 



7. 0004901 



8.0 



1.8061800 



2. 7092700 



3. 6123599 



4. 5154499 



5. 4I,S5399 



6.3216299 



7.2247199 



8.5 



1. 8588379 



2. 7882568 



3.7176757 



4. 6470946 



5. 5765136 



6. 5059325 



7. 43.53514 



9.0 



1. t'()84e50 



2. 8627275 



3. 8169700 



4. 7712125 



5. 7254551 



6. 6796976 



7. 6339401 



9.5 



1. 9554472 



2. 9331708 



3. 9108944 



4. 8886180 



5.8663416 



C. 8440652 



7. 8217888 



10.0 



2. OOCOOOO 



3. 0000000 



4. OOOOOOO 



5. OOOOOOO 



6. OOOOOOO 



7. OOOGOOO 



8. OOOOOOO 



10.5 



2. 0423786 



3. 0635679 



4.0647572 



5. 1059465 



6. 1271358 



7. 1483251 



8.1695144 



11.0 



2. 0827854 



3. 1241781 



4. 1655707 



5. 2069634 



6. 2483561 



7. 2897488 



8.3311415 



11.5 



2. 1213957 



3. 1820935 



4. 2427914 



5. .3034892 



6. 3641870 



7. 4248849 



8. 4855827 



12.0 



2. 1583G25 



3. 2375437 



4.31672,50 



5. 3959062 



6. 4750875 



7. 5542687 



8. 6334500 



12.5 



2. 1938200 



3. 2907300 



4. 3876401 



5. 4845501 



6.5814601 



7. 6783701 



8.7752801 



13.0 



2. 9.278867 



3. 3418301 



4. 4557734 



.5.5697168 



C. 6836601 



7. 7976035 



8.9115468 



13. 5 



2. 2606675 



3. 3910013 



4. 5213351 



5. 6510688 



6. 7820026 



7. 9123364 



9. 0426701 



14.0 



2. 2922561 



3. 4383841 



4. 5845121 



5. 7306402 



6. 8767683 



8. 0228962 



9. 1690243 



14.5 



2. 3227360 



3.4841040 



4. 6454720 



5. 8068400 



6. 96S20S0 



8. 1295760 



9. 2909440 



15.0 



2. 352182.5 



3. .5282738 



4. 7043650 



5. 8804.563 



7. 0565476 



8. 2326388 



9. 4087301 



15. 5 



2. 3806634 



3. 5709951 



4.7613268 



5. 9516585 



7. 1419902 



8.332.3219 



9. 5226536 



16.0 



2. 4082400 



3.6123599 



4. 8164799 



6. 0205999 



7.2247199 



8. 4288399 



9. 6329599 



If). 5 



2. 4349679 



3. 6524518 



4. 8699358 



6. 0874197 



7. 3049037 



8. 5223876 



9. 739871G 



17.0 



2. 4G08978 



3.0913468 



4. 9217957 



6. 1522446 



7. 3826935 



8. 6131424 



9. 8435914 



17.5 



2. 4860761 



3.7291141 



4. 9721522 



6.2151902 



7. 4582283 



8.7012663 



9. 9443044 



18.0 



2. 5105450 



3. 7658175 



5. 0210900 



6. 2763625 



7. 5316350 



8. 7869075 



10. 0421800 



J8.5 



2. 5343435 



3. 8015152 



5. 0686869 



6. 3358586 



7. 6030304 



8. 8702021 



10. 1373738 



19.0 



2. 5575072 



3. 8362608 



5.1150144 



6. 3937680 



7.072.5216 



8. 9512752 



10. 2300288 



19.5 



2. 5800692 



3.8701038 



.5. 1601384 



C. 4501731 



7. 7402077 



9. 0302423 



10. 3202769 



20.0 



2. G020600 



3. 9030900 



5. 2041200 



G. .5051500 



7. 8061800 



9. 1072100 



10. 4082400 



20.5 



2. 6235077 



3. 9352616 



5.2470154 



6. 5587693 



7. 8705232 



9. 1822770 



10. 4940309 



21.0 



2. 6444386 



3. 9666579 



5. 2888772 



6. 6110965 



7. 9333158 



9. 2555351 



10. 5777544 



21.5 



2.0648:69 



3. 9973154 



5. 3297538 



6. 6621923 



7. 9946308 



9. 3270692 



10. 6595077 



22.0 



2. 68484.'i4 



4. 0272680 



5. 369{iS07 



6.7121134 



8. 0545361 



9. 3969588 



10. 7393814 



22. 5 



2. 7043650 



4. 0565476 



5. 4087301 



6. 7609126 



8. 1130951 



9. 46.52776 



10. 8174601 



23.0 



2. 7234557 



4. 0851835 



5.4469113 



6. 8086392 



8. 1703670 



9. 5320949 



10. 8938227 



23.5 



2.7421357 



4.1132036 



5. 4842714 



6. 8553393 



8. 2-364072 



9. 59747.50 



10. 9685429 



24.0 



2. 7004225 



4. 1406337 



5. 5208450 



6. 9010562 



8. 2812675 



9. 6614787 



11.0416899 



24.5 



2. 7783322 



4. 1674983 



5. 5566643 



6. 9458304 



8. 3349965 



9. 7241626 



11. 1133287 



25.0 



2. 7958800 



4.1938200 



5. 5917600 



6. 9897000 



8. 3876401 



9. 7855801 



11. 1835201 



25.5 



2.8130804 



4. 2196205 



5. 6261607 



7. 0327009 



8.4392411 



9.84.57813 



11. 2.523214 



26.0 



2. 8299467 



4. 2449200 



5. 6598934 



7. 0748667 



8. 4898401 



9. 9048134 



11.3197868 



26.5 



2.8464917 



4. 2697376 



5. 6929835 



7. 1162294 



8. .5394752 



9.9627211 



11. 3859670 



27.0 



2. 8627275 



4. 2940913 



5. 7254551 



7.1568188 



8. 5881826 



10.019.5463 



11. 4509101 



27. 5 



2. 8786654 



4. 3179981 



5. 7573308 



7. 1966635 



8. 0359962 



10. 0753289 



11.5146016 



28.0 



2 8943161 



4. 3414741 



5. 7886321 



7. 2357902 



8. 6829482 



10. 1301062 



11. 5772643 



28.5 



2. 9096897 



4. 3645346 



5. 8193794 



7. 2742243 



8. 7290692 



10. 1839140 



11. 6387589 



29.0 



2. 9247960 



4. 3871940 



5. 8495920 



7.3119900 



8. 7743880 



10. 2367860 



11. 6991840 



29.5 



2. 939G440 



4. 4094660 



5. 8792881 



7.3491101 



8. 8189321 



10. 2887541 



11. 7585761 



30 



2. 9542425 



4. 4313638 



5. 9084850 



7. 3856063 



8. 8627275 



10. 3398488 



11. 8169700 



30.5 



2. 9685997 



4. 4.528995 



5. 9371994 



7. 4214992 



8. 9057990 



10. 3900989 



11. 8743987 



